Implementations of multiphysics simulation for MEMS by coupling single-physics solvers
DOI:
https://doi.org/10.1260/175095407782219201Abstract
Due to the growing demands from industries, the multiphysics simulation plays a more and more important role in the design of MEMS devices. This paper presents a fast convergence scheme which implements multiphysics simulation by coupling phenomena-specific single-physics solvers. The proposed scheme is based on the traditional staggered/relaxation approach but employs the Steffensen’s acceleration technique to speed up the convergence procedure. The performance of the proposed scheme is compared with three traditional techniques: the staggered/relaxation, the multilevel Newton and the quasi-Newton methods through several examples. The results show that this scheme is promising.
References
Senturia S.D., 1998. “CAD challenges for microsensors, microactuators, and microsystems”, Proceedings of the IEEE, 86(8), pp.1611–1626. https://doi.org/10.1109/5.704266
COMSOL, 2004. FEMLAB User’s Guide. COMSOL AB.
ANSYS, 2004. ANSYS User Manual. ANSYS, Inc., Canonsburg.
Cai X., Yie H., Osterberg P., et. al., 1993. “A relaxation/multipole-accelerated scheme for self-consistent electromechanical analysis of complex 3-D micromechanical structures”, Proceedings of the 1993 IEEE/ACM International Conference on Computer-Aided-Design, pp. 283–286. https://doi.org/10.1109/iccad.1993.580070
Senturia S.D., Aluru N.R., White J., 1997. “Simulating the behavior of MEMS devices: Computational methods and needs”, IEEE Computational Sci. & Eng. Magazine, 4(1), pp. 30–43. https://doi.org/10.1109/99.590854
Yie H., Cai X., White J., 1994. “Convergence properties of relaxation versus the surface-newton generalized- conjugate residual algorithm for self-consistent electromechanical analysis of 3-D micro-electro-mechanical structure”, Proceedings of IEEE NUPAD V, Honolulu, Hawaii, pp. 137–140. https://doi.org/10.1109/nupad.1994.343472
Aluru N.R., White J., 1999. “A multilevel Newton method for mixed-energy domain simulation of MEMS”, IEEE Journal of Microelectromechanical Systems, 8(3), pp. 299–308. https://doi.org/10.1109/84.788634
Kelley, C.T., 2003. Solving Nonlinear Equations with Newton’s Method, Philadelphia, U.S.: Society for Industrial and Applied Mathematics.
Senturia S.D., 2001. Microsystem Design, Kluwer Academic Publishers.
Lautrup B., 2005. “The PDE’s of Continuum Physics”, Proceedings of the Workshop on PDE methods in Computer Graphics, Copenhagen, Denmark.
Jin J.M., 1993. The Finite Element Method in Electromagnetics. New York: John Wiley & Sons.
ANSYS, 2004. ANSYS Coupled-Field Analysis Guide. ANSYS, Inc., Canonsburg.
Hibbit, 2004. ABAQUS User’s Manual. ABAQUS Inc.
Nabors K., Kim S., et. al., 1992. FastCap User’s Guide. Massachusetts Institute of Technology, Cambridge.
Rudin W., 1976. Principles of Mathematical Analysis. McGraw-Hill.
Mathews J.H., Fink K.D., 2004. Numerical Methods Using MATLAB, 4th Ed., Upper Saddle River, N.J.: Pearson Prentice Hall.
Kelley C.T., 1995. Iterative Methods for Linear and Nonlinear Equations, Philadelphia, U.S.: Society for Industrial and Applied Mathematics.
Knoll D.A., Keyes D.E., 2004. “Jacobian-free Newton-Krylov methods: a survey of approaches and applications”, Journal of Computational Physics, 193, pp. 357–396. https://doi.org/10.1016/j.jcp.2003.08.010
Shashkin, Y. A., 1991. Fixed Points. Providence, RI: Amer. Math. Soc.
Nievergelt Y., 1995. “The condition of Steffensen’s acceleration in several variables”, Journal of Computational and Applied Mathematics, 58(3), pp. 291–305.
Farhat C., Lesoinne M., et. al., 1998. “Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation,optimal discretization and application to aeroelasticity”, Computer Methods in Applied Mechanics and Engineering, 157(1–2), pp. 95–114. https://doi.org/10.1016/s0045-7825(97)00216-8
Cai X., Osterberg P., Yie H., et. al., 1994. “Self-consistent electromechanical analysis of complex 3-D microelectro-mechanical structures using relaxation/multipole-accelerated method”, Sensors Materials, 6(2), pp. 85–99. https://doi.org/10.1109/iccad.1993.580070
Osterberg P.M., Senturia S.D., 1997. “M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures”, IEEE Journal of Microelectromechanical Systems, 6(2), pp. 107–118. https://doi.org/10.1109/84.585788
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